Why Are ‘American Options’ More Difficult to Price than ‘European Options’?

American options are more difficult to price because they grant the holder the right to exercise the option at any time up to and including the expiration date. European options can only be exercised at expiration.

The possibility of early exercise in American options introduces an additional, complex variable that requires numerical methods (like binomial trees or finite difference methods) rather than a simple closed-form solution like the Black-Scholes model.